Showing posts with label variable. Show all posts
Showing posts with label variable. Show all posts

Thursday, January 20, 2022

Factor Analysis Principal Components Analysis

 


Factor analysis (FA) is a statistical method of reducing a large set of data to a smaller set by identifying patterns in the data that have common characteristics. Factor analysis is sometimes called data reduction or dimension reduction.

The original numerical values in the data set are observed variables (also called manifest variables) such as the items in a large survey or test. Factor analysis may find patterns characterized by a shared statistical relationship representing a factor, which is also called a dimension. A researcher examines the content of the items linked to this factor and chooses a factor label such as verbal skills for related items on an intelligence test.

The factors may be treated as variables in additional research. These are secondary variables. Because they are created from the observed variables, they are considered latent variables. For example, if 5 items on a personality test are associated with one factor labeled "agreeableness" then agreeableness is a latent variable.

The set of identified factors is referred to as the structure of the data set. If the data are from a test then researchers refer to the structure of the test.

Factors are identified based on the variance they account for in the data. The amount of variance explained by a factor is represented by an eigenvalue. Researchers look for eigenvalues of 1.0 or more to consider a factor to be a valuable contribution to explaining the underlying structure of a data set.

Not all factors are equal. That is, when more than one factor have been identified, they will contribute differently to explaining the variance in the data set.


Different kinds of Factor Analysis

Exploratory Factor Analysis (EFA). When researchers do not know the structure of a data set, they use EFA to discover the set of factors.

Confirmatory Factor Analysis (CFA).  When researchers wish to test a hypothesis about a data set, they perform CFA. For example, if they believe their forgiveness questionnaire contains one factor called forgiveness, they can examine the structure to see if one factor best accounts for the data set. If one factor is the best solution then they have found support for their hypothesis.

Principal Components Analysis (PCA) is a common form of confirmatory factor analysis. 

Factor Analysis is important to understanding tests in Counseling and Psychotherapy. See

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Factor Analysis is often used to reduce the data collected from survey research. 

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You can read many published articles at no charge:

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Friday, May 7, 2021

Continuous variables in behavioral research

 

Continuous variable. A variable having a wide range of numerical values, such as intelligence, achievement, and personality variables.

Example: Scores on a Big Five test of personality are often reported as T-Scores for each of the five scales. Most people obtain scores in the range of 40 to 60 but it is possible to obtain lower and higher scores. The point of the example is that the scores are continuous and cover a wide range. 

Researchers can group people based on their scores using groups labels like "high" and "low" perhaps by deciding that the median would be the score to separate high and low scores. Changing the continuous variable results in the formation of a grouping variable or categorical variable.

Example 2: Age is a continuous variable beginning at birth and continuing to death. Researchers can group people by age and create a grouping or categorical value.

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Please check out my website   www.suttong.com

   and see my books on   AMAZON       or  GOOGLE STORE

Also, consider connecting with me on    FACEBOOK   Geoff W. Sutton    

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You can read many published articles at no charge:

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Confounding variables in behavioral research

 

A Confounding variable is a variable that produces unexpected changes in the dependent variable and therefore interferes with interpreting the capacity of an independent variable to produce or explain changes in a dependent variable.

Example: During a study of anxiety that includes measures of anxiety and stress, some participants watch a documentary about the treatment of anxiety and some do not. Documentary-watching may confound the results if watching the program influenced the scores on the measures of anxiety and stress. Similarly, some participants may be exposed to a source of stress in their environment but others are not, which could interfere with interpreting the results.


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Please check out my website   www.suttong.com

   and see my books on   AMAZON       or  GOOGLE STORE

Also, consider connecting with me on    FACEBOOK   Geoff W. Sutton    

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You can read many published articles at no charge:

  Academia   Geoff W Sutton     ResearchGate   Geoffrey W Sutton 


Categorical or Grouping variable in Behavioral Research

 

Categorical variables are those variables having two or more groups or levels such as sex, ethnicity, and religious group. 

They may be called independent variables even though they are not true independent variables under experimental control.

Categorical variables, also called grouping variables, can be created from continuous variables. For example, researchers often obtain the age of their study participants. Age is a continuous variable but sometimes, researchers group ages together and compare how people of different age groups answer questions on a survey.


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Please check out my website   www.suttong.com

   and see my books on   AMAZON       or  GOOGLE STORE

Also, consider connecting with me on    FACEBOOK   Geoff W. Sutton    

   TWITTER  @Geoff.W.Sutton    

You can read many published articles at no charge:

  Academia   Geoff W Sutton     ResearchGate   Geoffrey W Sutton 


Thursday, January 14, 2021

Independent Variable IV

 


Independent variable (IV). The variable in a research study that a researcher manipulates to determine if another variable, the dependent variable, changes when the IV changes.

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Dependent Variable DV

 


Dependent variable (DV). The variable in a research study that is expected to change when a researcher varies the level of an independent variable.

Example: In a counseling study designed to help people forgive, forgiveness would be the DV and the survey used to measure forgiveness would be the Dependent Measure.

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Tuesday, January 5, 2021

ANCOVA in Counseling & Behavioral Research

 


ANCOVA


ANCOVA is a procedure like ANOVA except researchers can study the effects of one or more independent variables on a dependent variable after adjusting for other variables, called covariates, which were not a primary focus of the study. The letter C in ANCOVA stands for covariate. There can be several covariates in a study. In testing for differences among groups experiencing different leadership styles, we could study the effects on employee satisfaction after adjusting for a covariate of years of employment. A key word in ANCOVA studies is adjusting. Analysts adjust the scores based on information about the covariate before testing for significant differences.


Basic features of an ANCOVA:


Independent or grouping Variable = 1 or more

Dependent or criterion Variable = 1

Covariates = 1 or more


An test indicates significance overall and for specific effects or relationships.

A commonly reported measure of effect size is eta squared.

value reveals the probability of a significant relationship-- one that is not due to chance factors.

Read more about ANCOVA in the following books.


Applied Statistics Concepts for Counselors on AMAZON or GOOGLE






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MORE about ANCOVA and COVARIANCE


Analysis of Covariance

Geoffrey W. Sutton, Ph.D.

            The analysis of covariance is a research strategy that is based upon a two or more groups design that yields at least interval data and could be analyzed using ANOVA. We use the term ANCOVA as an acronym. The letter C in the acronym represents a covariate. We usually refer to the covariate as a CV. A covariate is a variable that is significantly correlated with the dependent variable.

 In experimental research, the covariate helps reduce error variance and makes the F-test more sensitive to any main or interaction effects. The correlation between the covariate and the DV allows for the removal of the effects of a CV on a DV and represents a known source of systematic bias. 

In nonexperimental research, researchers can use the covariate to statistically remove the influence of a variable to help equate groups that could not be formed by random assignment or to better understand another relationships of interest. 

A third purpose is to examine group differences by controlling for the influence of a DV when there are several DVs in an analysis. This latter use is known as multivariate analysis of variance or, MANCOVA.

 You can use more than one CV in a research design or ANCOVA procedure. However, if there is a correlation greater than r =  .80 between two CVs, you should use only one of the CVs because they appear to be measuring a lot of the same variance.

  As with all statistical procedures, there are several assumptions to meet. The first three are basic assumptions for ANOVA and the next three are additional assumptions for ANCOVA.

1. All data are from random samples and independent of other data.

2. The scores on the DV are normally distributed in the population.

3. The distributions of scores on the DV have equal variances.

            Additional assumptions for ANCOVA

4. There is a linear relationship between the CV and the DV.

5. The slope for the regression line (for the CV) is the same in each group.

6. The CV has high reliability and was measured without error.

Research questions and hypotheses

 We generally use a key phrase to identify the CV in a research study. That key phrase can be controlling for or adjusted for. Here are some examples.

1. What is the difference between memory scores for people with right and left hemisphere stroke when adjusted for age?

2. What is the effect of a marriage enrichment program when controlling for years of marriage?

The research hypothesis states there is an effect or a difference when adjusting for the CV and the null hypothesis assumes the usual no difference, or no effect result, when adjusting for the CV.

Following is a hypothesis based on question number one.

H1: When adjusting for age, there is a significant difference between the means on verbal memory between patients who experience right and left hemisphere strokes.

H01: When adjusting for age, there is no significant difference between the means on verbal memory in the population between patients who experienced right and left hemisphere strokes (p < .05).

The research method with a CV

 We would follow usual procedures for delivering the IV (independent variable) or measuring a QIV (quasi-independent variable) along with the DVs. We would consider what variables might affect the DVs and collect data to measure those CVs. After all the data have been entered into our database, we would obtain the descriptive statistics. Next, make any adjustments to the data and calculate correlations between the measured variables. Those variables that were not the primary focus of the experiment or study will be entered as CVs in the ANOVA procedure if they are highly correlated with the DVs. We will perform the usual post hoc analyses, if applicable.

Results

When interpreting the results of an ANCOVA, we will refer to the adjusted means. SPSS reports the results of the analysis. In the Test of Between Subjects Effects table, SPSS reports the CV along with an F-test. If the CV made a significant contribution to the analysis, the p-value for the CV will be less than .05 (or your preferred level of significance). The output will also include adjusted and unadjusted means. When reporting the results, you should report both sets of means. In a small study, the means can be reported in a paragraph. In a larger study, the means should be placed in a table.

Example of ANCOVA reporting for a fictitious study.

IV = communication skills training vs. a no skills training control (2 groups)

DV = some measure of communication on a continuous scale

CV = years of employment-- a continuous scale

Workplace communication skills training for employees significantly improved positive statements when adjusted for years of employment, F(2,38) = 4.56, p = .03, eta2 = .42, Observed Power = .67.

 

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Chi-Square

 

Chi-Square is a statistical test that can be used to analyze results from categorical variables. Categorical variables are variables that contain clearly different groups. The chi-square statistic is used with frequency data. 


The chi-square value is reported with a probability (p) value indicating significance. 


For example, we can use chi-square to test for an association between frequency of attendance at organizational meetings and age groups (category variable). 


Common measures of effect size associated with chi-square analyses are Cramer’s V or the phi coefficient.


Read more about Chi Square and other statistics in the following books.



Applied Statistics: Concepts for Counselors on AMAZON or GOOGLE









Creating Surveys on AMAZON    or   GOOGLE  Worldwide










Links to Connections

 

Please check out my website   www.suttong.com

   and see my books on   AMAZON       or  GOOGLE STORE

Also, consider connecting with me on    FACEBOOK   Geoff W. Sutton    

   TWITTER  @Geoff.W.Sutton    

You can read many published articles at no charge:

  Academia   Geoff W Sutton     ResearchGate   Geoffrey W Sutton 


Regression Data Analysis

 

Regression is a statistical procedure used to predict values on a criterion variable from the knowledge of values obtained on a predictor variable. For example, an organization may use an employment screening test or survey that has been useful in the past to predict how well employees perform a particular type of job. The criterion variable is a continuous variable, meaning it can have a range of score values. Predictor variables may be either continuous or categorical variables. When there is only one predictor variable and one criterion variable, the procedure is known as simple regression.

 

Read more about regression in these books.


Applied Statistics on AMAZON or GOOGLE











Creating Surveys on AMAZON or GOOGLE












Checkout My Page   www.suttong.com

  

My Books  AMAZON       and           GOOGLE STORE

 

FOLLOW me on

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Articles:

   Academia   Geoff W Sutton   

 

   ResearchGate   Geoffrey W Sutton 


Adult Decision Making Competence ADMC

  Measure name: Adult Decision-Making Competence ADMC Overview: The Adult Decision-Making Competence measure consists of a set of seven d...